Beable-guided measurement theory

Abstract

In quantum mechanics, randomness is postulated as a separate axiom. De Broglie's theory allows one to reproduce quantum phenomena from completely deterministic formalism. But the question of the quantum randomness emergency in the de Broglie-Bohm theory needs special attention. In the work [G. Tastevin, F. Lalo\"e, Comptes Rendus. Physique, 2021, 22, 1, pp. 99-116], it was shown that it arises as a result of the device microscopic state influence on the measurement result. In our work, we investigate the genesis of the quantum randomness in the de Broglie's theory in more details. Namely, we investigate the target system and the device behaviour in the decoherence process and model the measurement of canonical-conjugate observables. We propose a thought experiment which tests the opportunity of the information transition using beable-parameters violating the uncertainty relation. We show that in the measurement process, the strong stochastic fluctuations of beable parameters arise randomising the system in accordance with the uncertainty relation. Nevertheless, we find anomalous models of measurement in which these fluctuations can be neglected. These special models require further investigation.